Three men using efforts of 600N 500N and 400N respectively push a drum of 240kg up an inclined plane whose angle of inclination is 30° What is the efficiency of the plane

Answer 1

To find the efficiency of the inclined plane, we need to compare the work done by the plane to the work done by the three men.

The work done by a force is given by the equation: work = force * distance * cos(angle)

Let's calculate the work done by each man and the total work done by the three men:
Work1 = 600N * distance * cos(30°)
Work2 = 500N * distance * cos(30°)
Work3 = 400N * distance * cos(30°)
Total work done by the three men = Work1 + Work2 + Work3

Since we have the weight of the drum (240kg), we can calculate the distance moved up the inclined plane using trigonometry.
The weight component along the inclined plane is given by the equation: weight_component = weight * sin(angle)

Weight component of the drum = 240kg * 9.8m/s^2 * sin(30°)
Distance = Weight component / (total force applied by the three men) = (240kg * 9.8m/s^2 * sin(30°)) / (600N + 500N + 400N)

Now, let's calculate the work done by the inclined plane:
Work done by the plane = weight of the drum * distance * cos(30°) = (240kg * 9.8m/s^2) * distance * cos(30°)

Finally, we can calculate the efficiency of the inclined plane using the equation:
Efficiency = (work done by the plane) / (total work done by the three men)

By substituting the values and calculating, we can find the efficiency.